Modifiers in the Monolith of Fate are special effects that make Echoes more difficult in various different ways and more rewarding by providing Increased Item Rarity and experience gained, similar to Corruption. The difference with modifiers is that they last from 1 to 3 Echoes total instead of globally to all Echoes, have varies different effects and aren't usually simply just more monster damage and health. Stacking several modifiers will further increase the difficult and rewards.
More challenging modifiers provide higher benefits. Experience bonuses from Monolith of Fate modifiers and corruption does not apply to characters below level 50.